Modal decomposition and equivalent circuit representations of lossless coupled multiwire lines

Equivalent circuit representations and propagation modes on lossless coupled n-wire transmission-lines are assumed to satisfy Telegrapher's equations presented by the matrix partial differential equations. It is shown that the equivalent circuit for the n-wire line can be represented to be a cascade connection of Ideal transformer Interconnections (ITI), a set of n transmission lines (in the mode space) and ITI. The transformation matrix for the ITI can be classified into three types: (A) an orthogonal matrix, (B) a product of diagonal and orthogonal matrices, and (C) a product of orthogonal, diagonal and orthogonal matrices. Three kinds of characteristic impedances are described: n characteristic impedances for n lines in the mode space, the characteristic impedance matrix and nxn characteristic wire impedances. It is also shown that the bi-orthogonality of propagation is satisfied among voltage propagation modes and current propagation modes. An even mode and an odd mode supported on a symmetrical two-wire line are extended into propagation modes on n-wire lines, and a voltage even mode and current odd modes are obtained.